Saturday, 12 August 2017

On This Day in Math - August 12

I belong to those theoreticians who know by direct observation what it means to make a measurement. Methinks it were better if there were more of them.
~Erwin Schrodinger

The 224th day of the year; 224 is the sum of the cubes of 4 consecutive integers:
224 = 23 + 33 + 43 + 53 and also 23 + 63

Cool thing about 224: 224 = 23+45+67+89 *Derek Orr ‏@Derektionary

Every number smaller than 224 can be expressed as the sum of distinct divisors of 224.

EVENTS

1269 A letter written on this day by Master Peter de Maricourt (Perigrinus) indicates that he had a knowledge of magnetic polarity, knew that opposites attract, understood that splitting a bar magnet preserved two poles in each part, and was aware that a weaker magnet could have its polarity reversed by a stronger one.*A history of physics in its elementary branches By Florian Cajori

1654 Earliest known Solar Eclipse map, by Erhard Weigel. According to German historian of science Klaus-Dieter Herbst, this map of the total solar eclipse of August 12, 1654 was published by Erhard Weigel on the day before the eclipse! On the right is a reconstruction of the map using modern eclipse calculations and geographic information system software. The map applies an orthographic projection from the moon’s perspective at the time of greatest eclipse. *eclipse-maps.com 1755 19 year old Joseph Louis Lagrange sends a letter to Euler where he described his "method of variations". *Optimal Control and Forecasting Euler responded promptly,and with great fervor and the two began a long series of correspondence. "You seem to have brought the theory of maxima and minima almost to its highest degree of perfection." Euler also promoted the admission of Lagrange to the Berlin Academy. 1877 Asaph Hall discovered Deimos, outer satellite of Mars. It is named after Deimos, a figure representing dread or terror in Greek Mythology. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik
In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars. " *assorted 1883 Fragmented Comet Nearly Hits The Earth: On 12th and 13th August 1883, an astronomer at a small observatory in Zacatecas in Mexico made an extraordinary observation. José Bonilla counted some 450 objects, each surrounded by a kind of mist, passing across the face of the Sun. Today, Hector Manterola at the National Autonomous University of Mexico in Mexico City, gave a different interpretation. He thinks Bonilla must have been seeing fragments of a comet that had recently broken up. This explains the 'misty' appearance of the pieces and why they were so close together. Manterola and co end their paper by spelling out just how close Earth may have come to catastrophe that day. They point out that Bonilla observed these objects for about three and a half hours over two days. This implies an average of 131 objects per hour and a total of 3275 objects in the time between observations.
Each fragment was at least as big as the one thought to have hit Tunguska. Manterola and co end with this: "So if they had collided with Earth we would have had 3275 Tunguska events in two days, probably an extinction event." *MIT Technology Review, (Many question the interpretation)1949 On Aug. 12, 1949, time slowed briefly in London. Fifty starlings settled on Big Ben’s minute hand and delayed the striking of the hour by four and a half minutes. *Greg Ross, Futility Closet (A “murmuration” of starlings, as this phenomenon is known, must be one of the most magical, yet underrated, wildlife spectacles on display in winter. Impenetrable as the flock’s movements might seem to the human eye, the underlying maths is comparatively straightforward. Each bird strives to fly as close to its neighbors as possible, instantly copying any changes in speed or direction. As a result, tiny deviations by one bird are magnified and distorted by those surrounding it, creating rippling, swirling patterns. In other words, this is a classic case of mathematical chaos (larger shapes composed of infinitely varied smaller patterns). Whatever the science, however, it is difficult for the observer to think of it as anything other than some vast living entity. Until recently such sights were common over London. *Daniel Butler, Telegraph, 23 Feb 2009) 1985 Celebration of the centenary of the International Statistical Institute in Amsterdam begins. It lasted until August 22. *VFR
2014 BBC announces the first Female Fields Medal winner. An Iranian mathematician working in the US has become the first ever female winner of the celebrated Fields Medal. In a landmark hailed as "long overdue", Prof Maryam Mirzakhani was recognised for her work on complex geometry. Four of the medals were presented in Seoul at the International Congress of Mathematicians, *BBC 2026 Next total solar eclipses in Europe, total in North of Spain shortly before sunset *NSEC

BIRTHS

1769 Johann Christian Martin Bartels (12 August 1769 – 7/20 December 1836) was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan. *Wik 1862 Jules Antoine Richard (12 August 1862 in Blet, Département Cher,- 14 October 1956) Richard worked mainly on the foundations of mathematics and geometry, relating to works by Hilbert, von Staudt and Méray.
Further according to Richard, it is the aim of science to explain the material universe. And although non-Euclidean geometry had not found any applications (Albert Einstein finished his general theory of relativity only in 1915), Richard already stated clairvoyantly:"One sees that having admitted the notion of angle, one is free to choose the notion of straight line in such a way that one or another of the three geometries is true." *Wik 1887 Erwin Schrodinger, born (12 August 1887 – 4 January 1961). Austrian theoretical physicist who shared the 1933 Nobel Prize for Physics with the British physicist P.A.M. Dirac. Schrödinger took de Broglie's concept of atomic particles as having wave-like properties, and modified the earlier Bohr model of the atom to accommodate the wave nature of the electrons. This made a major contribution to the development of quantum mechanics. Schrödinger realized the possible orbits of an electron would be confined to those in which its matter waves close in an exact number of wavelengths. This condition, similar to a standing wave, would account for only certain orbits being possible, and none possible in between them. This provided an explanation for discrete lines in the spectrum of excited atoms. *TIS 1897 Otto Struve (August 12, 1897 – April 6, 1963) Ukrainian-Russian-American astronomer who spent most of his life and his entire scientific career in the United States.
He was one of the few eminent astronomers in the pre-Space Age era to publicly express a belief that extraterrestrial intelligence was abundant, and so was an early advocate of the search for extraterrestrial life.
"An intrinsically improbable event may become highly probable if the number of events is very great. ... [I]t is probable that a good many of the billions of planets in the Milky Way support intelligent forms of life. To me this conclusion is of great philosophical interest. I believe that science has reached the point where it is necessary to take into account the action of intelligent beings, in addition to the classical laws of physics."
Struve received the Gold Medal of the Royal Astronomical Society (1944), the Bruce Medal (1948), the Henry Draper Medal (1949), and the Henry Norris Russell Lectureship of the American Astronomical Society (1957)
The crater Struve on the Moon (commemorating three of the Struve astronomers), Asteroid 2227 Otto Struve and the Otto Struve Telescope of McDonald Observatory are named in his honor. *TIA 1908 Caryl Parker Haskins (August 12, 1908 to October 8, 2001) was a scientist, author, inventor, philanthropist, governmental adviser and pioneering entomologist in the study of ant biology. In the 1930s he was inspired by Alfred Lee Loomis to establish his own research facility. Along with Franklin S. Cooper, he founded the Haskins Laboratories, a private, non-profit research laboratory, in 1935. Affiliated with Harvard University, MIT, and Union College in Schenectady, NY, Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of this program is now part of Pace University in New York. In the 1940s Luigi Provasoli joined the Laboratories to set up a research program in marine biology which disbanded with his retirement in 1978. Since the 1950s, the main focus of the research of Haskins Laboratories has been on speech and its biological basis. The main facility of Haskins Laboratories moved to New Haven, Connecticut in 1970 where it entered into affiliation agreements with Yale University and the University of Connecticut. Haskins Laboratories continues to be a leading, multidisciplinary laboratory with an international scope that does pioneering work on the science of the spoken and written word.
Haskins served as President, Research Director, and Chairman of the Board of Haskins Laboratories, 1935-'87; Director, E.I. du Pont de Nemours, 1971-'81 and Research Professor, Union College, 1937-'55. In 1956, he was appointed to the Presidency of the Carnegie Institution of Washington, a position he held until 1971. He was also President of the Sigma Xi society in 1967-'68. He remained a Trustee of Carnegie Institution and of Haskins Laboratories, as well as Trustee Emeritus of the National Geographic Society until his death.[2] He also continued his research on entomology, working with his wife, Edna Haskins, and other colleagues. *Wik 1919 Eleanor Margaret Burbidge, née Peachey, FRS (August 12, 1919 Davenport, England - ) is a British-born American astrophysicist, noted for original research and holding many administrative posts, including director of the Royal Greenwich Observatory.
During her career, she served at the University of London Observatory, Yerkes Observatory of the University of Chicago, Cavendish Laboratory in Cambridge, England, the California Institute of Technology, and from 1979 to 1988 was first director of the Center for Astronomy and Space Sciences at the University of California at San Diego (UCSD), where she has worked since 1962.
After receiving her Ph.D. in 1943, she started to research galaxies by linking a spectrograph to telescopes. At the Yerkes Observatory in the USA her work involved studying B stars and galaxy structure.
In 1957, the B²FH group showed the famous result that all of the elements except the very lightest, are produced by nuclear processes inside stars. For this they received the Warner Prize in 1959. In her later research she was one of the first to measure the masses and rotation curves of galaxies and was one of the pioneers in the study of quasars.
At UCSD she also helped develop the faint object spectrograph in 1990 for the Hubble Space Telescope. Currently, she is a professor emeritus of physics at UCSD and continues to be active in research, such as engaging in non-standard cosmologies such as, intrinsic redshift.*Wik 1926 Horace Chandler Davis (born August 12, 1926, Ithaca, New York) is an American-Canadian mathematician, writer, and educator.
He was born in Ithaca, New York, to parents Horace B. Davis and Marian R. Davis. In 1948 he married Natalie Zemon Davis; they have three children.
In 1950 he received a doctorate in mathematics from Harvard University.
His principal research investigations involve linear algebra and operator theory in Hilbert space. Furthermore he has made contributions to numerical analysis, geometry, and algebraic logic. He is one of the eponyms of the Davis–Kahan theorem and Bhatia–Davis inequality (along with Rajendra Bhatia). The Davis-Kahan-Weinberger dilation theorem is one of the landmark results in the dilation theory of Hilbert space operators and has found applications in many different areas. A PhD thesis titled "Backward Perturbation and Sensitivity Analysis of Structured Polynomial Eigenvalue Problem" is dedicated to this theorem. In total Chandler Davis has written around eighty research papers in mathematics.
He is currently one of the co-Editors-in-Chief of the Mathematical Intelligencer. In 2012 he became a fellow of the American Mathematical Society.

He began his writing career in Astounding Science Fiction in 1946. From 1946 through 1962 he produced a spate of science fiction stories, mostly published there. One of the earliest, published May 1946, was The Nightmare, later the lead story in A Treasury of Science Fiction, edited by Groff Conklin; it argued for a national policy of decentralizing industry to evade nuclear attacks by terrorists. He also issued the fanzine "Blitherings" in the 1940s.

Davis came from a radical family and has identified himself as a socialist and former member of the Communist Party of America.
Davis—along with two other professors, Mark Nickerson and Clement Markert—refused to cooperate with the House Unamerican Activities Committee and was subsequently dismissed from the University of Michigan. Davis was then sentenced to a six-month prison term where he was able to do some research. A paper from this era has the following acknowledgement:

"Research supported in part by the Federal Prison System. Opinions expressed in this paper are the author's and are not necessarily those of the Bureau of Prisons."

The Federal government released Davis from prison in 1960. After his release, Davis moved to Canada, where he currently resides. He began teaching at the University of Toronto. He has lived in Canada longer than he lived in the US.

In 1991, the University of Michigan Senate initiated the annual Davis, Markert, Nickerson Lecture on Academic and Intellectual Freedom. Recent speakers have included: Cass Sunstein (2008), Nadine Strossen (2007), Bill Keller (2006), Floyd Abrams (2005), and Noam Chomsky (2004). *Wik 1930 Jacques Tits (12 August 1930; ) is a Belgian and French mathematician who works on group theory and geometry and who introduced Tits buildings, the Tits alternative, and the Tits group. Tits was an "honorary" member of the Nicolas Bourbaki group; as such, he helped popularize Harold Scott MacDonald Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph.
He received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction "Pour le Mérite". In 2008 he was awarded the Abel Prize, along with John Griggs Thompson, “for their profound achievements in algebra and in particular for shaping modern group theory." *Wik

DEATHS

1900 James Edward Keeler (September 10, 1857 – August 12, 1900) was an American astronomer who confirmed Maxwell's theory that the rings of Saturn were not solid (requiring uniform rotation), but composed of meteoric particles (with rotational velocity given by Kepler's 3rd law). His spectrogram of 9 Apr 1895 of the rings of Saturn showed the Doppler shift indicating variation of radial velocity along the slit. At the age of 21, he observed the solar eclipse of July, 1878, with the Naval Observatory expedition to Colorado. He directed the Allegheny Observatory (1891-8) and the Lick Observatory from 1898, where, working with the Crossley reflector, he observed large numbers of nebulae whose existence had never before been suspected. He died unexpectedly of a stroke, age 42.*TIS 1901 Ernest de Jonquières (3 July 1820 Carpentras, France – 12 Aug 1901 Mousans-Sartoux, France) was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU 1989 William B. Shockley (February 13, 1910 – August 12, 1989) English-American engineer and teacher, co-winner (with John Bardeen and Walter H. Brattain) of the Nobel Prize for Physics in 1956 for their development of the transistor, a device that largely replaced the bulkier and less-efficient vacuum tube and ushered in the age of microminiature electronics. *TIS 2004 Sir Godfrey Newbold Hounsfield (28 August 1919 – 12 August 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. *TIS
2007 Ralph Asher Alpher (February 3, 1921 – August 12, 2007) was an American cosmologist. Alpher's dissertation in 1948 dealt with a subject that came to be known as Big Bang nucleosynthesis. In a strange mathematical pun, his pre-publication of his thesis may have caused his independent role to have been minimized.
Although his name appears on the paper, Hans Bethe had no direct part in the development of the theory, although he later worked on related topics; Gamow added his name to make the author list Alpher, Bethe, Gamov, a pun on alpha, beta, gamma (α, β, γ), the first three letters of the Greek alphabet. Thus, Alpher's independent dissertation was first published on April 1, 1948 in the Physical Review with three authors. The humor engendered by the prodigious Gamow may at times have obscured the critical role Alpher played in developing the theory. This seminal paper was based on his dissertation (defended shortly thereafter).
With the award of the 2005 National Medal of Science, Alpher's original contributions (nucleosynthesis and the cosmic microwave background radiation predicition) to the modern big bang theory are beginning to receive due recognition. Neil deGrasse Tyson was instrumental in a NSF committee recommendation.
In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. Ralph Alpher died following an extended illness on August 12, 2007. He had been in failing health since falling and breaking his hip in February 2007. *Wik

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I'm a retired math teacher, calc-stats-the regular stuff... Interested in Math, math history, and assorted other curiosities.Married and in love with a gorgeous woman. I have a math page on the etymology of math terms, and another, On This Day in Math, which covers historical events related to the current date.